When federal prosecutors recommended a substantial prison term for President Trump’s former lawyer, Michael D. Cohen, they linked Mr. Trump to the crimes Mr. Cohen had committed in connection with the 2016 presidential campaign.

What the prosecutors did not say in Mr. Cohen’s sentencing memorandum filed on Friday, however, is that they have continued to scrutinize what other executives in the president’s family business may have known about those crimes, which involved hush-money payments to two women who had said they had affairs with Mr. Trump.

After Mr. Cohen pleaded guilty in August to breaking campaign finance laws and other crimes — he will be sentenced on Wednesday — the federal prosecutors in Manhattan shifted their attention to what role, if any, Trump Organization executives played in the campaign finance violations, according to people briefed on the matter.

Mr. Cohen, Mr. Trump’s self-described fixer, has provided assistance in that inquiry, which is separate from the investigation by the special counsel, Robert S. Mueller III.

In addition to implicating Mr. Trump in the payments to the two women, Mr. Cohen has told prosecutors that the company’s chief financial officer was involved in discussions about them, a claim that is now a focus of the inquiry, according to the people, who spoke on the condition of anonymity because the investigation is continuing.

Mr. Cohen has told prosecutors that he believes Mr. Trump personally approved the company’s decision to reimburse him for one of the payments, one of the people said.

Neither the chief financial officer, Allen Weisselberg, nor any other executives at the Trump Organization have been accused of wrongdoing, and there is no indication that anyone at the company will face charges in connection with the inquiry.

But in recent weeks, the prosecutors contacted the company to renew a request they had made this year for documents and other materials, according to the people. The precise nature of the materials sought was unclear, but the renewed request is further indication that prosecutors continue to focus on the president’s company even as the case against Mr. Cohen comes to a close, the people said.

At the time of the payments to the two women, Mr. Trump was the head of the company, and although he turned over its management to his elder sons, he still owns it through a trust. While the prevailing view at the Justice Department is that a sitting president cannot be indicted, the prosecutors in Manhattan could consider charging him after leaving office. It is also possible the prosecutors could seek his testimony before he leaves office if they continue the investigation into anyone else who might have had a role in the crimes, a person briefed on the matter said.

A spokeswoman for the Trump Organization did not respond to requests for comment.

A spokesman for the federal prosecutors in Manhattan, the United States attorney’s office for the Southern District of New York, declined to comment. A lawyer for Mr. Weisselberg, Mary E. Mulligan, also declined to comment, as did Guy Petrillo, a lawyer for Mr. Cohen.

In early September, before Mr. Cohen had completed his discussions with prosecutors and before the Southern District renewed its record request, Bloomberg reported that the Southern District was investigating Trump Organization executives other than Mr. Cohen.

Last month, Mr. Cohen unexpectedly struck a plea deal with Mr. Mueller over a new charge that he lied to Congress about plans to build a Trump Tower in Moscow during the 2016 presidential campaign. In a court filing the following day, Mr. Cohen’s lawyers highlighted how he had spoken on numerous occasions to each of the prosecutorial agencies investigating Mr. Trump or his company.

Mr. Cohen has told the Southern District prosecutors that he arranged the hush money to the two women at the direction of Mr. Trump. In the filing on Friday, the Southern District prosecutors put the weight of their office behind Mr. Cohen’s admission, saying that “with respect to both payments, he acted in coordination with and at the direction of” Mr. Trump.

The Southern District’s filing also said Mr. Cohen had provided potentially “useful information about matters relating to ongoing investigations being carried out by this office.” It added that prosecutors “assessed Cohen to be forthright and credible, and the information he provided was largely consistent with other evidence gathered,” a potentially problematic sign for the Trump Organization.

Though Mr. Trump’s lawyers declined to comment, people close to Mr. Trump argue that Mr. Cohen would not be sentenced now if he had substantially more to offer to investigators — and they note that the Southern District memo cited Mr. Cohen’s “pattern of deception that permeated his professional life.” What’s more, people who have worked for the Southern District have said that prosecutors might say things in a sentencing memo that they would not try to pursue as a separate case.

Mr. Trump lashed out at Mr. Cohen on Twitter in recent days, saying, “He lied for this outcome and should, in my opinion, serve a full and complete sentence.”

One of the campaign finance charges Mr. Cohen pleaded guilty to centered on Mr. Cohen’s paying $130,000 to the adult film actress Stormy Daniels, who said she had an affair with Mr. Trump. The payment amounted to an excessive contribution to Mr. Trump’s campaign, prosecutors said, arguing that her silence helped his election chances and that campaign finance law prohibits individuals from donating more than $2,700 to a presidential candidate in the general election.

Mr. Cohen also pleaded guilty to “causing” an illegal corporate donation to Mr. Trump when he urged American Media Inc., which publishes The National Enquirer, to buy the rights to a former Playboy model’s story of an affair with Mr. Trump. The deal effectively silenced the model, Karen McDougal, for the remainder of the campaign.

Mr. Cohen has also told the Southern District that Mr. Weisselberg, who is one of Mr. Trump’s longtime loyalists, was involved in discussions about how to pay Ms. Daniels, according to a person briefed on the matter. Mr. Cohen linked him to the deal with American Media as well.

During the campaign, Mr. Cohen recorded a conversation he had with Mr. Trump about buying the rights to negative information American Media had collected on Mr. Trump. Mr. Cohen told Mr. Trump, who did not know he was being recorded, that “I’ve spoken to Allen Weisselberg about how to set the whole thing up.” The deal was signed by American Media and Mr. Cohen, according to court papers. But a person familiar with the arrangement said that Mr. Trump balked at reimbursing America Media, as had been agreed to, and the media company was never reimbursed in relation to Ms. McDougal.

But after the campaign, Mr. Weisselberg handled reimbursing Mr. Cohen for the payment to Ms. Daniels, according to people briefed on the matter. In early 2017, Mr. Cohen sought to recoup the $130,000 he paid out of his own pocket to Ms. Daniels as well as $50,000 he spent on a technology company in connection with the campaign, prosecutors have said.

Not only did the Trump Organization repay those expenses, but it agreed to pay taxes Mr. Cohen might have incurred on the reimbursements. This decision to “gross up” Mr. Cohen went against the Trump Organization’s typical reimbursement practices, people briefed on the matter said.

The company also agreed to pay Mr. Cohen a $60,000 bonus. (Mr. Cohen left the company once Mr. Trump became president). In total, the company paid Mr. Cohen $420,000, doled out in monthly installments of $35,000. In internal documents, the company “falsely accounted” for the payments as “legal expenses,” when, in fact, they were campaign expenditures, prosecutors say.

Mr. Weisselberg spoke with prosecutors this year from the Southern District when they were investigating Mr. Cohen. It is unclear what he said, and it is believed that he spoke on the condition that his statements could not be used against him.

One person familiar with Mr. Weisselberg’s work at the Trump Organization, who was not authorized to speak on his behalf, suggested that he might not have known the purpose of Mr. Cohen’s reimbursements, noting that Mr. Cohen often did personal legal work for the president and his family. That kind of work was generally performed with few, if any, questions asked, the person said.

Rebecca R. Ruiz contributed reporting.

A version of this article appears in print on , on Page A1 of the New York edition with the headline: Done With Cohen, U.S. Inquiry Digs Deeper Into Trump Business. Order Reprints | Today’s Paper | Subscribe